Question

from 1990 to 2000, the number of thousand visits by people to hawaii volcanoes national park increased by about 43.1 thousand visits. per year. In 2000, there were about 1529.6 thousand visits to the park. write an equation that gives the number of thousand visits as a function of the number of years since 1990.

Answer 1

Let n be the thousands of visitors
Let x be the number of years since 1990

n(x) then produces the number of visitors in any given year since 1990. We are told that in 2000 (10 years after 1990)

n(10) = 1529.6
n(x+10) = 1529.6 + 43.1x

That gives us the visitors for years after 2000. But we want to back up to 1990. SO substitute (x-10) for x to get

n(x-10+10) = 1529.6 + 43.1(x-10)
n(x) = 1529.6 + 43.1x - 431
n(x) = 1098.6 + 43.1x

Makes sense, since during the first 10 years, 431 visitors are added, making the count 1529.6 in 2000. And things just keep going from there.